Can I delete or move a resource plot within my town?

The resource plots in the town are in fixed positions. The resource producing buildings that you unlock and place have to be put in a range of set locations around the plots. Once placed you cannot delete them but you can move them, however only to one of the other specific set locations for it.

To move it (the same as any other building) you tap and hold on it for a second until the option to move appears. You can then drag it to one of the other set locations.